SEM approach to the transient scattering by an inhomogeneous, lossy dielectric slab; Part 1: The homogeneous case

Abstract

In two companion papers, the singularity expansion method is applied to the computation of the transient scattering of a pulsed electromagnetic wave of finite duration by an isotropic, inhomogeneous, lossy dielectric slab. The time-domain electric field is expressed as a Laplace inversion integral over the Bromwich contour. Conditions for the validity of a representation in terms of natural-mode quantities only are derived, i.e. for a vanishing integral along the closing contour in the left halfplane, the latter being the contribution from the essential singularity at infinity. In the present paper, this procedure is first carried out for a homogeneous slab. For that case, an alternative method exists where the computation of the integral along the closing contour is reduced to a modification of the residual contributions from the poles and the numerical evaluation of a principal-value integral along the branch cut of the complex index of refraction. This method applies when the closing conditions are violated. The location of the poles is computed numerically by determining the zero's of the analytically known slab-denominator with the aid of Muller's root-finding procedure. In the subsequent summation of the residual contributions, acceleration of the convergence is carried out to allow for discontinuities in the incident-pulse shape. Some numerical results are presented and discussed.